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Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control
Michael Sebek
https://arxiv.org/abs/2506.08034 https://

Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control
We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we examine left and right fraction representations of transfer functions, showing that right zeros correspond to similarity classes of quaternionic matrix right eigenvalues. We then propose a feedback design procedure that generalizes pole placement to quaternions - a…